What is the three variable percent equation?
Every basic percent problem can be written as a single proportion: part / whole = percent / 100. This is often described in words as "is over of equals percent over one hundred." Because there are three unknowns and one equation, if you know any two of them you can always solve for the third. This calculator does exactly that — you supply two numbers, choose which value is missing, and it returns the answer along with the complete set of values.
How to use it
First select what you want to solve for: Percent, Part, or Whole. Then fill in the two known fields and leave the unknown one blank. Click calculate and the tool applies the appropriate rearrangement of the formula. The result box shows the solved value, and the table below restates all three numbers so you can confirm the proportion balances.
The formula explained
Starting from $$\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}$$ simple algebra gives three rearrangements:
• To find the percent: \(\text{percent} = (\text{part} \div \text{whole}) \times 100\).
• To find the part: \(\text{part} = \text{whole} \times \text{percent} \div 100\).
• To find the whole: \(\text{whole} = \text{part} \times 100 \div \text{percent}\).
The calculator picks the right one based on your selection and guards against division by zero.
Worked example
Suppose 25 students out of a class scored an A and you want the percentage. Here the part is 25 and the whole is 200. Solving for percent: $$(25 \div 200) \times 100 = 12.5\%$$ If instead you knew the percentage was 12.5% and the whole was 200, solving for the part gives $$200 \times 12.5 \div 100 = 25.$$
FAQ
What if I want a percent increase or decrease? This tool solves the basic proportion. For change, compute the difference first, then use that as the part.
Can the part be larger than the whole? Yes — that simply produces a percent greater than 100, which is valid.
Why is my answer zero? Solving for percent or whole requires a non-zero denominator; if the relevant divisor is blank or zero the result is shown as zero.
